proofs/containers/balanced_search_tree/navm.bend checks
raw source on the hub · import bend-collections-laws-containers@1.0.0.0/proofs/containers/balanced_search_tree/navm.bend as Navm
19 imports
import Base import ../../lib/logic.bend as L import ../../lib/nat.bend as N import ../../lib/list.bend as LL import ../../lib/order.bend as O import ../../../spec/lib/common.bend as SC import ../../../spec/containers/balanced_search_tree/main.bend as S import ../../../src/containers/balanced_search_tree.bend as M import ./nbr.bend as NB import ./state.bend as ST import ./mirror.bend as MI import ./tree.bend as TR import ./find.bend as FI import ./reads.bend as RD import ./ends.bend as EN import ./path.bend as P import ./nav.bend as NV import ./navs.bend as NS import ../../lib/nat_list.bend as NL
Templates
template keq_fst source · line 51 · raw
@-K:Data -> @-V:Data -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+xs:List<&2, Nat> -> @+h:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, xs, nl, pl) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.key_m(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(xs)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(xs)))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_key(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(xs))) : Maybe<&2, K>}
template keq_last source · line 58 · raw
@-K:Data -> @-V:Data -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+xs:List<&2, Nat> -> @+h:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, xs, nl, pl) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.key_m(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(xs)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(xs)))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_key(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(xs))) : Maybe<&2, K>}
template keq_pk source · line 65 · raw
@-K:Data -> @-V:Data -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+h:Bool -> @+a:List<&2, Nat> -> @+b:List<&2, Nat> -> @+ha:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, a, nl, pl) == True{} : Bool} -> @+hb:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, b, nl, pl) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.key_m(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(a), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(b))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(a), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(b))))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_key(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(a), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(b)))) : Maybe<&2, K>}
template keq_eq source · line 73 · raw
@-K:Data -> @-V:Data -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+i:Nat -> @+l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+r:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+h:Bool -> @+incl:Bool -> @+hi:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.key_m(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, i), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, i))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_key(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, i)) : Maybe<&2, K>} -> @+hx:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)), nl, pl) == True{} : Bool} -> @+hy:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/ends.oks(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c)), nl, pl) == True{} : Bool} -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.key_m(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)))))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)))))))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_key(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l))))))) : Maybe<&2, K>}
template keq_c source · line 80 · raw
@-K:Data -> @-V:Data -> @-cmp:(@_:K -> @_:K -> Cmp) -> @+nl:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.Node<K>> -> @+pl:List<&2, Maybe<&2, V>> -> @+c:List<&2, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.Fr> -> @+i:Nat -> @+l:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+r:0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.Tr -> @+k:K -> @+h:Bool -> @+incl:Bool -> @+ihl:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.key_m(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl)))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_key(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl))) : Maybe<&2, K>} -> @+ihr:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.key_m(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl)), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl)))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_key(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl))) : Maybe<&2, K>} -> @+he:{0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.key_m(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)))))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)))))))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_key(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l))))))) : Maybe<&2, K>} -> @+cc:Cmp -> {0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/containers/balanced_search_tree/main.key_m(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ent(K, V, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/tree.pk3(Nat, cc, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l))))))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pv(V, pl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/tree.pk3(Nat, cc, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l))))))))) == 0x5c489f5d9646d7cc9aa3dd8137e9dc07/src/containers/balanced_search_tree.node_key(K, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.nd(K, nl, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/tree.pk3(Nat, cc, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, l, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, True{}, r} <> c, nl, k, h, incl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/nav.gnav(K, cmp, r, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.FR{i, False{}, l} <> c, nl, k, h, incl), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, incl, i, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.pk(Nat, h, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.fst0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(r), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.after(c))), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.last0(0x5c489f5d9646d7cc9aa3dd8137e9dc07/spec/lib/common.append(Nat, 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/path.before(c), 0x5c489f5d9646d7cc9aa3dd8137e9dc07/proofs/containers/balanced_search_tree/state.ids(l)))))))) : Maybe<&2, K>}